9. Find the compound ratio of each of the following pairs of ratios.
(1) 13 : 9 and 27: 26
(ii) 6:11 and 22 : 15
(ii) 75 cm : 1 m 25 cm and 10: 7.50 (iv) 2 kg : 480 g and 2 h : 2 h 30 min
please give the process in copy and take a picture and correct answer only
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Answers
Step-by-step explanation:
Given :-
(1) 13 : 9 and 27: 26
(ii) 6:11 and 22 : 15
(iii) 75 cm : 1 m 25 cm and 10: 7.50
(iv) 2 kg : 480 g and 2 h : 2 h 30 min
To find :-
Find the compound ratio of each of the following pairs of ratios.
Solution :-
Given ratios are :
The compound ratio = Product of the antecedents: Product of the consequents
I)13 : 9 and 27: 26
Product of antecedents = 13×27 = 351
Product of the consequents = 9×26 = 134
Their ratio = 351 : 134
The compound ratio = 351:134
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ii)6:11 and 22 : 15
Product of antecedents = 6×22 = 132
Product of the consequents =11×15 = 165
Their ratio = 132 : 165
=> 132/165
=> 12/15
=> 4/5
=> 4:5
Their ratio = 4:5
The compound ratio = 4:5
_____________________________
iii)75 cm : 1 m 25 cm and 10: 7.50
1 m = 100 cm
1 m 25 cm = 100+25= 125 cm
=> 75 : 125 and 10: 7.50
Product of antecedents = 75×10 = 750
Product of the consequents =125×7.50= 937.50
Their ratio = 750 : 937.50
=> 750/937.50
=> 750/(93750/100)
=> (750×100)/93750
=> 75000/93750
=> 7500/9375
=> 300/375
=> 12/15
=> 4/5
Their ratio = 4:5
The compound ratio = 4:5
______________________________
iv) 2 kg : 480 g and 2 h : 2 h 30 min
We know that
1 kg = 1000 g
=> 2kg = 2000 g
1 hour = 60 min
2 hours = 120 min
=> 2000:480 and 120 : 150
Product of antecedents = 2000×120=240000
Product of the consequents =480×150=72000
Their ratio = 240000:72000
=> 240000/72000
=> 240/72
=> 10/3
=> 10:3
The compound ratio = 10:3
_____________________________
Answer:-
I)The compound ratio of 13 : 9 and 27: 26 is
351 : 134
ii)The compound ratio of 6:11 and 22 : 15 is 4:5
iii)The compound ratio of 75 cm : 1 m 25 cm and 10: 7.50 is 4:5
iv)The compound ratio of 2 kg : 480 g and 2 h : 2 h 30 min is 10:3
Used formulae:-
- The compound ratio of two ratios is the ratio of the Product of the antecedents to the Product of the consequents
- The compound ratio of a:b and c:d is ac:bd
Points to remember :-
- An ordered comparision of the same quantities is called the ratio.
- The ratio of a and b is a:b
- In a:b , a is called antecedent and b is called antecedent
- a:b can be written as a/b
- Inverse ratio of a:b is b:a